## Meshless methods: An overview and recent developments.(English)Zbl 0891.73075

Summary: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enable $$p$$-adaptivity to be achieved. Methods for constructing discontinuous approximations and approximations with discontinuous derivatives are also described. Next, several issues in implementation are reviewed: discretization (collocation and Galerkin), quadrature in Galerkin and fast ways of constructing consistent moving least-squares approximations. The paper concludes with some sample calculations.

### MSC:

 74S30 Other numerical methods in solid mechanics (MSC2010) 76M25 Other numerical methods (fluid mechanics) (MSC2010) 74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids 76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics

DYNA3D; LS-DYNA
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